Estimation and Inference for Stochastic Volatility Models with Heavy-Tailed Distributions Staff working paper 2026-8 Gabriel Rodriguez Rondon, Jean-Marie Dufour, Md. Nazmul Ahsan Statistical inference--both estimation and testing--for stochastic volatility (SV) models is known to be challenging and computationally demanding. We propose simple and efficient estimators for SV models with conditionally heavy-tailed error distributions, particularly the Student’s t and Generalized Exponential Distributions (GED). The estimators rely on a small set of moment conditions derived from ARMA-type representations of SV models, with an option to apply “winsorization” to improve stability and finite-sample performance. Except for the degrees of-freedom parameter, closed-form expressions are available for all other parameters, extending Ahsan and Dufour (2019, 2021), thus eliminating the need for numerical optimization or initial values. We derive the estimators’ asymptotic distribution and show that, due to their analytical tractability, they support reliable, and even exact, simulation-based inference via Monte Carlo or bootstrap methods. We assess their performance through extensive simulations and demonstrate their practical relevance in financial return data, which strongly reject the normality assumption in favor of heavy-tailed models. Content Type(s): Staff research, Staff working papers JEL Code(s): C, C1, C12, C13, C15, C2, C22, C5, C51, C53, C58 Research Theme(s): Financial markets and funds management, International markets and currencies, Models and tools, Econometric, statistical and computational methods, Economic models
MSTest: An R-Package for Testing Markov Switching Models Staff working paper 2026-7 Gabriel Rodriguez Rondon, Jean-Marie Dufour We present the R package MSTest, which implements hypothesis testing procedures to determine the number of regimes in Markov switching models. The package provides several testing frameworks, including Monte Carlo likelihood ratio tests, moment-based tests, parameter stability tests, and classical likelihood ratio procedures. Content Type(s): Staff research, Staff working papers JEL Code(s): C, C1, C12, C15, C18, C6, C63, C8, C87 Research Theme(s): Models and tools, Econometric, statistical and computational methods, Economic models, Monetary policy, Real economy and forecasting
Partial Identification of Heteroskedastic Structural Vector Autoregressions: Theory and Bayesian Inference Staff working paper 2025-14 Helmut Lütkepohl, Fei Shang, Luis Uzeda, Tomasz Woźniak We consider structural vector autoregressions that are identified through stochastic volatility. Our analysis focuses on whether a particular structural shock can be identified through heteroskedasticity without imposing any sign or exclusion restrictions. Content Type(s): Staff research, Staff working papers JEL Code(s): C, C1, C11, C12, C3, C32, E, E6, E62 Research Theme(s): Models and tools, Econometric, statistical and computational methods, Economic models, Monetary policy, Real economy and forecasting
Unmet Payment Needs and a Central Bank Digital Currency Staff discussion paper 2023-15 Christopher Henry, Walter Engert, Alexandra Sutton-Lalani, Sebastian Hernandez, Darcey McVanel, Kim Huynh We discuss the payment habits of Canadians both in the current payment environment and in a hypothetical cashless environment. Content Type(s): Staff research, Staff discussion papers JEL Code(s): C, C1, C12, C9, E, E4, O, O5, O54 Research Theme(s): Money and payments, Cash and bank notes, Digital assets and fintech, Retail payments
Private Digital Cryptoassets as Investment? Bitcoin Ownership and Use in Canada, 2016-2021 Staff working paper 2022-44 Daniela Balutel, Walter Engert, Christopher Henry, Kim Huynh, Marcel Voia We report on the dynamics of Bitcoin awareness and ownership from 2016 to 2021, using the Bank of Canada's Bitcoin Omnibus Surveys (BTCOS). Our analysis also helps understand Bitcoin owners who adopted during the COVID-19 and how they differ from long-term owners. Content Type(s): Staff research, Staff working papers JEL Code(s): C, C1, C12, E, E4, O, O5, O51 Research Theme(s): Models and tools, Econometric, statistical and computational methods, Money and payments, Digital assets and fintech
October 12, 2022 Five things we learned about Canadian Bitcoin owners in 2021 Daniela Balutel, Walter Engert, Christopher Henry, Kim Huynh, Marcel Voia We present key findings from the 2021 Bitcoin Omnibus Survey on Canadians’ awareness and ownership of Bitcoin. Most Canadians have heard of Bitcoin, which remains primarily used as an investment. Ownership jumped in 2021, reflecting increased savings during the pandemic and greater availability of user-friendly platforms to buy Bitcoin. Content Type(s): Publications, Financial System Hub articles JEL Code(s): C, C1, C12, E, E4, O, O5, O51
Cash, COVID-19 and the Prospects for a Canadian Digital Dollar Staff discussion paper 2022-17 Walter Engert, Kim Huynh We provide an analysis of cash trends in Canada before and during the COVID-19 pandemic. We also consider the potential two scenarios for issuance of a central bank digital currency in Canada: the emergence of a cashless society or the widespread use of an alternative digital currency in Canada. Finally, we discuss the Canadian experience in maintaining cash as an efficient and accessible method of payment and store of value. Content Type(s): Staff research, Staff discussion papers JEL Code(s): C, C1, C12, C9, E, E4, O, O5, O54 Research Theme(s): Money and payments, Cash and bank notes, Digital assets and fintech
Cash in the Pocket, Cash in the Cloud: Cash Holdings of Bitcoin Owners Staff working paper 2022-26 Daniela Balutel, Christopher Henry, Kim Huynh, Marcel Voia We estimate the effect that owning Bitcoin has on the amount of cash held by Canadian consumers. Our results question the view that adopting certain new technologies, such as Bitcoin, leads to a decline in cash holdings. Content Type(s): Staff research, Staff working papers JEL Code(s): C, C1, C12, E, E4, O, O3, O33, O5, O51 Research Theme(s): Models and tools, Econometric, statistical and computational methods, Money and payments, Cash and bank notes, Digital assets and fintech
Bitcoin Awareness, Ownership and Use: 2016–20 Staff discussion paper 2022-10 Daniela Balutel, Marie-Hélène Felt, Gradon Nicholls, Marcel Voia In this paper, we examine trends in Canadian ownership of Bitcoin and other cryptocurrencies from 2016 to 2020 using data from surveys conducted by the Bank of Canada. Content Type(s): Staff research, Staff discussion papers JEL Code(s): C, C1, C12, E, E4, O, O5, O51 Research Theme(s): Money and payments, Cash and bank notes, Digital assets and fintech
Cash and COVID-19: What happened in 2021 Staff discussion paper 2022-8 Heng Chen, Walter Engert, Kim Huynh, Daneal O’Habib, Joy Wu, Julia Zhu Using data from the Bank Note Distribution System and consumer surveys, we find that bank notes in circulation remained high through 2021. Canadians continued to rely on electronic methods of payment, but a significant share also continued using cash for payments. Content Type(s): Staff research, Staff discussion papers JEL Code(s): C, C1, C12, C9, E, E4, O, O5, O54 Research Theme(s): Money and payments, Cash and bank notes, Retail payments